Can you repeat a portion of a texture across a face?
You can use some math nodes and keep simple proportions for you texture parts (for instance working with 1/2 or 1/4... easy to multiply or divide).

Here is an example :



Each face is assigned to a material composed of nodes like these ones (this material is for the red triangles) :




Amount of repeats
Shift U as the triangle starts at U = 0.5
Don't shift V as the triangle starts at V = 0
Modulos : here the texture is divided in 2 (so modulo = 1/2)
Shift back U to 0.5
Shift back V (but V starts at 0)


For the blue square, you may invert the roles for U and V.

For the green circle, just don't shift anything.

To reach the upper right quadrant, shift both U and V 0.5.